.TH "SRC/dlaed1.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dlaed1.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdlaed1\fP (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info)"
.br
.RI "\fBDLAED1\fP used by DSTEDC\&. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix\&. Used when the original matrix is tridiagonal\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlaed1 (integer n, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq, double precision rho, integer cutpnt, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

.PP
\fBDLAED1\fP used by DSTEDC\&. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix\&. Used when the original matrix is tridiagonal\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLAED1 computes the updated eigensystem of a diagonal
 matrix after modification by a rank-one symmetric matrix\&.  This
 routine is used only for the eigenproblem which requires all
 eigenvalues and eigenvectors of a tridiagonal matrix\&.  DLAED7 handles
 the case in which eigenvalues only or eigenvalues and eigenvectors
 of a full symmetric matrix (which was reduced to tridiagonal form)
 are desired\&.

   T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)

    where Z = Q**T*u, u is a vector of length N with ones in the
    CUTPNT and CUTPNT + 1 th elements and zeros elsewhere\&.

    The eigenvectors of the original matrix are stored in Q, and the
    eigenvalues are in D\&.  The algorithm consists of three stages:

       The first stage consists of deflating the size of the problem
       when there are multiple eigenvalues or if there is a zero in
       the Z vector\&.  For each such occurrence the dimension of the
       secular equation problem is reduced by one\&.  This stage is
       performed by the routine DLAED2\&.

       The second stage consists of calculating the updated
       eigenvalues\&. This is done by finding the roots of the secular
       equation via the routine DLAED4 (as called by DLAED3)\&.
       This routine also calculates the eigenvectors of the current
       problem\&.

       The final stage consists of computing the updated eigenvectors
       directly using the updated eigenvalues\&.  The eigenvectors for
       the current problem are multiplied with the eigenvectors from
       the overall problem\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
         The dimension of the symmetric tridiagonal matrix\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
         On entry, the eigenvalues of the rank-1-perturbed matrix\&.
         On exit, the eigenvalues of the repaired matrix\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is DOUBLE PRECISION array, dimension (LDQ,N)
         On entry, the eigenvectors of the rank-1-perturbed matrix\&.
         On exit, the eigenvectors of the repaired tridiagonal matrix\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
         The leading dimension of the array Q\&.  LDQ >= max(1,N)\&.
.fi
.PP
.br
\fIINDXQ\fP 
.PP
.nf
          INDXQ is INTEGER array, dimension (N)
         On entry, the permutation which separately sorts the two
         subproblems in D into ascending order\&.
         On exit, the permutation which will reintegrate the
         subproblems back into sorted order,
         i\&.e\&. D( INDXQ( I = 1, N ) ) will be in ascending order\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is DOUBLE PRECISION
         The subdiagonal entry used to create the rank-1 modification\&.
.fi
.PP
.br
\fICUTPNT\fP 
.PP
.nf
          CUTPNT is INTEGER
         The location of the last eigenvalue in the leading sub-matrix\&.
         min(1,N) <= CUTPNT <= N/2\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (4*N + N**2)
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (4*N)
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit\&.
          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
          > 0:  if INFO = 1, an eigenvalue did not converge
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA 
.br
 Modified by Francoise Tisseur, University of Tennessee 
.RE
.PP

.PP
Definition at line \fB161\fP of file \fBdlaed1\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.